Using bosonic codes as the physical qubits for a fault-tolerant quantum computing architecture provides two tiers of protection from noise.
The first comes from the bosonic code itself.
GKP qubits possess a degree of intrinsic robustness to those bosonic noise channels that result in small displacements (relative to the \(\sqrt{\pi }\)  lattice spacing) in phase space.
This includes weak levels of photon loss, the dominant error mode for quantum communication [1]}, [2]}.
Any shift that is less than half the lattice spacing (\(\sqrt{\pi }/2\) ) can be corrected by non-destructively measuring the GKP stabilizers—which are \(2\sqrt{\pi }\)  shifts in either position or momentum.
This CV error-correction procedure outputs continuous syndrome data, which can be used to undo the displacement with the help of a decoder.
Noise that leads to larger displacements can result in errors that are undetectable by measuring only the GKP qubit stabilizers.
In the fault-tolerant regime, these larger displacements are much less likely to occur, and so occasional errors on GKP qubits can be corrected by applying the second layer of protection: a qubit quantum error-correcting code.
Implementing these codes requires only Clifford gates and Pauli measurements, both of which are easy (Gaussian) for the GKP qubit encoding.
